CN114612609A - Curved surface reflection line calculation method, device, computer equipment and storage medium - Google Patents

Abstract

The invention provides a curved surface reflection line calculation method, a curved surface reflection line calculation device, computer equipment and a storage medium, wherein the method comprises the steps of determining a plane triangle; constructing a first space curve corresponding to each side of a plane triangle; acquiring coordinates and normal vectors of all points forming a first space curve; constructing a plurality of second space curves and third space curves based on the coordinates and normal vector lines of each point of each first space curve corresponding to the plane triangle; dividing the area where the plane triangle is located into a plurality of plane sub-triangles based on the second space curves and the third space curves; acquiring rays; determining a planar sub-triangle intersecting the ray; and calculating the reflected ray of the intersection point position of the ray on the plane sub-triangle by using the reflection law. The method for reconstructing the curved surface by using the vertex coordinates and the normal vector of the plane triangle and calculating the light reflected by the curved surface makes the constructed curve smoother and makes the calculated reflected light more accurate.

Description

Curved surface reflection line calculation method, device, computer equipment and storage medium

technical field

The invention relates to the technical field of ray reflection line calculation on a curved surface, in particular to a calculation method, device, computer equipment and storage medium for a curved surface reflection line.

Background technique

In 3D geometric modeling, the target surface is usually discretized into a large number of triangular and quadrilateral plane elements. For the target surface, the number of surfels is large enough to approximate the original surface sufficiently. When the number of target subdivisions is not so sufficient, in some scenarios, the curved surface needs to be reconstructed based on the current planar metamodel to improve the model representation accuracy. In addition, when a beam of light strikes a real surface (such as a spherical surface), the distribution of its reflected rays is continuous in space; if the surface is represented by a subdivided plane element, no matter how finely the surface is subdivided, its The distribution of reflected light is also spatially discontinuous. The reason is that the normal vector of the plane element is unique, and the normal vector of the original surface where the plane element is located is different everywhere and continuously distributed in space. Therefore, when calculating the reflection of light on the surface, in order to improve the calculation accuracy and approximate the real situation, it is also necessary to reconstruct the surface and solve the intersection of the ray and the surface and the reflected light.

In 2015, the book "Finite Element Analysis: ANSYS Theory and Applications: 4th Edition", published by Electronic Industry Press, deduces a method for reconstructing triangular planar elements into triangular surfaces, which uses shape functions to reconstruct surfaces in known In the case of the upper 6 points, any point on the reconstructed surface can be calculated, that is, the reconstructed surface can be obtained. The problem with this method is that it is not easy to maintain continuity between adjacent reconstructed surfaces, or even if they are continuous, the target surface composed of reconstructed surfaces is not easy to keep smooth, resulting in a large error in calculating the reflected rays of rays on the target surface. .

SUMMARY OF THE INVENTION

Based on this, it is necessary to provide a method, device, computer equipment and storage medium for calculating the reflection line of a curved surface in view of the above technical problems.

A method for calculating the reflection line of a curved surface, comprising:

Determine the plane triangle;

constructing a first space curve corresponding to each side of the plane triangle;

obtaining the coordinates and normal vectors of each point forming the first space curve;

A plurality of second space curves and third space curves are constructed based on the coordinates and normal vector lines of each point of each of the first space curves corresponding to the plane triangle, wherein the endpoints of both ends of each of the second space curves are located at on two adjacent first space curves;

dividing the area where the plane triangle is located into a plurality of plane sub-triangles based on each of the second space curves and each of the third space curves;

get rays;

determining the planar sub-triangle intersecting the ray;

The reflected ray at the intersection of the ray on the plane sub-triangle is calculated using the law of reflection.

In one of the embodiments, the step of constructing the first space curve corresponding to each side of the plane triangle includes:

Calculate the normal vectors of the three vertices of the planar triangle;

The first space curve corresponding to the sides of the plane triangle is constructed according to the coordinates and normal vectors of the vertices of the sides of the plane triangle.

In one of the embodiments, the step of constructing the first space curve corresponding to the sides of the plane triangle according to the coordinates and normal vectors of the vertices of the sides of the plane triangle includes:

Taking the coordinates of the vertices of the sides of the plane triangle as the two endpoints of the first line segment, performing normal vector interpolation along one end of the first line segment to the other end to obtain a first normal vector surface;

Based on the first normal vector surface, a space curve prediction is performed to construct the first space curve.

In one of the embodiments, the step of performing spatial curve prediction based on the first normal vector surface, and constructing the first spatial curve further includes:

Error correction is performed on the constructed first space curve.

In one of the embodiments, the step of constructing a plurality of second space curves and third space curves based on the coordinates and normal vector lines of each point of each of the first space curves corresponding to the plane triangle includes:

Extract a point from the first space curve corresponding to the two sides of the plane triangle as a line segment endpoint, and connect the two line segment endpoints to obtain a connecting line segment;

constructing a second space curve corresponding to the connecting line segment based on the connecting line segment and the coordinates and normal vectors of the line segment endpoints of the connecting line segment;

A point is extracted from each of the two adjacent second space curves as a line segment endpoint, and the two line segment endpoints are connected to obtain a construction line segment;

Based on the construction line segment and the coordinates and normal vectors of the line segment endpoints of the construction line segment, a third space curve corresponding to the construction line segment is constructed.

In one of the embodiments, the step of calculating the reflected ray at the intersection of the ray on the plane sub-triangle using the law of reflection includes:

Calculate the surface normal vector of the intersection of the ray and the plane sub-triangle;

Based on the surface normal vector at the intersection position and the ray, the reflection law is used to calculate the reflected ray at the intersection position of the ray on the plane sub-triangle.

A curved surface reflection line calculation device, comprising:

The plane triangle determination module is used to determine the plane triangle;

a first space curve building module, configured to build a first space curve corresponding to each side of the plane triangle;

a first coordinate and normal vector acquisition module, used to acquire the coordinates and normal vectors of each point forming the first space curve;

The second space curve building module is configured to build a plurality of second space curves and third space curves based on the coordinates and normal vector lines of each point of each of the first space curves corresponding to the plane triangle, wherein each of the The end points of both ends of the second space curve are located on two adjacent first space curves, and the end points of both ends of each of the third space curves are located on two adjacent second space curves;

a sub-triangle dividing module, configured to divide the area where the plane triangle is located into a plurality of plane sub-triangles based on each of the second space curves and each of the third space curves;

A ray acquisition module for acquiring rays;

an intersecting sub-triangle determination module, configured to determine a plane sub-triangle intersecting with the ray;

The reflected ray calculation module is configured to use the reflection law to calculate the reflected ray at the intersection of the ray on the plane sub-triangle.

In one of the embodiments, the first space curve building module includes:

a vertex normal vector calculation unit for calculating the normal vectors of the three vertices of the plane triangle;

A first space curve construction unit, configured to construct a first space curve corresponding to the sides of the plane triangle according to the coordinates and normal vectors of the vertices of the sides of the plane triangle.

A computer device, comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, when the processor executes the computer program, the processor implements the steps in any of the above-mentioned methods for calculating curved surface reflection lines .

A computer-readable storage medium on which a computer program is stored, and when the computer program is executed by a processor, implements the steps of any one of the above-mentioned methods for calculating curved surface reflection lines.

The above-mentioned method, device, computer equipment and storage medium for calculating the reflection line of a curved surface use the vertex coordinates and normal vectors of a plane triangle to reconstruct the surface and calculate the light reflected on the curved surface, so that the constructed curve is smoother, so that the calculated The reflected rays are more accurate, and are used in the surface reconstruction process of 3D geometric models composed of flat triangles, and subsequent scenes that require calculation of the intersection of rays and surfaces or reflected rays.

Description of drawings

1 is a schematic flowchart of a method for calculating a curved surface reflection line in one embodiment;

Fig. 2 is a structural block diagram of a curved surface reflection line computing device in one embodiment;

Fig. 3 is the internal structure diagram of the computer device in one embodiment;

4 is a schematic diagram of a process of constructing a space curved surface based on a plane triangle in one embodiment;

5 is a schematic diagram of the intersection of a ray and a space curve and a reflected ray in one embodiment;

6 is a schematic diagram of a normal vector reconstruction process on one side of a planar triangle in one embodiment;

7 is a schematic diagram of spatial curve prediction in one embodiment;

8 is a schematic diagram of a spatial curve error correction process in one embodiment;

9 is a schematic diagram of the normal vector of a point inside a triangle in one embodiment;

10 is a schematic flowchart of a method for calculating a curved surface reflection line in another embodiment;

FIG. 11 is a schematic diagram of a common vertex planar triangle in one embodiment.

Detailed ways

In order to make the purpose, technical solutions and advantages of the present application more clearly understood, the present application will be described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application, but not to limit the present application.

Example 1

In this embodiment, as shown in FIG. 1 , a method for calculating a curved surface reflection line is provided, which includes:

Step 110, determine a plane triangle.

In this embodiment, as shown in FIG. 4( a ), the planar triangle is a triangle determined based on a two-dimensional space, and the planar triangle is located on a plane determined by the X axis and the Y axis in FIG. 4 .

Step 120, constructing a first space curve corresponding to each side of the plane triangle.

In this embodiment, as shown in (a) and (b) of FIG. 4 , curves are respectively constructed for each side of the plane triangle, each curve corresponds to one side of the triangle, and each curve and one side of the triangle are in the same plane.

Step 130: Obtain the coordinates and normal vectors of each point forming the first space curve.

In this embodiment, the coordinates and normal vectors of each point on each first space curve are acquired.

Step 140: Construct a plurality of second space curves and third space curves based on the coordinates and normal vector lines of each point of each of the first space curves corresponding to the plane triangle, wherein two of the second space curves are The end points of the ends are located on two adjacent first space curves, and the end points of both ends of each of the third space curves are located on two adjacent second space curves.

In this embodiment, as shown in (c) of FIG. 4 , the points on the two adjacent sides of the plane triangle are used as the two end points of the second space curve to construct the second space curve; The points on the second space curve serve as two endpoints of the third space curve, and the third space curve is constructed.

Step 150: Divide the area where the plane triangle is located into a plurality of plane sub-triangles based on each of the second space curves and each of the third space curves.

In this embodiment, the projections of each of the second space curves and each of the third space curves on a plane triangle intersect, and the plane triangle is corresponding to each of the second space curves and each of the third space curves The original space surface of is divided into multiple planar sub-triangles.

In this embodiment, each second space curve and each third space curve divide the plane triangle into a plurality of sub-triangles, that is, plane sub-triangles, and the plane sub-triangles are also called plane small triangles or small triangles. It should be understood that the two ends of the second space curve are located on two adjacent sides of the plane triangle, respectively. Therefore, the second space curves spanning different sides intersect, so that the plane triangle is divided into a plurality of plane subsections. triangle.

It should be understood that, taking a space sphere with a radius R as an example, the sphere is usually divided into a large number of "plane triangles" for approximate representation in a computer. In this way, the original smooth curved surface is replaced by a large number of "flat triangles", resulting in discontinuity of reflected light from the target surface. In this application, an attempt is made to reconstruct the original curved surface (in this case, a spherical surface) corresponding to the planar triangle based on any one of the "planar triangles". Specifically, the set of plane sub-triangles divided by the second space curve and the third space curve is an approximate representation of the original surface corresponding to the plane triangle. The purpose is to improve the accuracy of the intersection of the ray and the original surface. Triangle intersection to approximate the intersection of the ray with the original surface.

Step 160, acquiring rays.

In this embodiment, the ray is an incident light ray, the trajectory of the ray is obtained, and the incident direction and position of the ray are obtained.

Step 170: Determine the plane sub-triangles intersecting the ray.

In this embodiment, based on the direction and position of the ray, as shown in (a) and (b) in FIG. 5 , the plane sub-triangle intersected by the ray can be determined.

Step 180: Calculate the reflected ray at the intersection of the ray on the plane sub-triangle by using the law of reflection.

In this embodiment, as shown in FIG. 5( c ), the reflection law is used to calculate the path of the reflected ray formed by the reflection of the ray on the intersecting plane sub-triangles, and the reflection direction and position of the reflected ray are calculated.

In one embodiment, the step of constructing the first space curve corresponding to each side of the plane triangle includes: calculating normal vectors of three vertices of the plane triangle; according to the coordinates of the vertices of the sides of the plane triangle and the normal vector to construct the first space curve corresponding to the sides of the plane triangle.

In one embodiment, the step of constructing the first space curve corresponding to the sides of the plane triangle according to the coordinates and normal vectors of the vertices of the sides of the plane triangle includes: using the sides of the plane triangle The coordinates of the vertex of the first line segment are taken as the two end points of the first line segment, and normal vector interpolation is performed along one end of the first line segment to the other end to obtain the first normal vector surface; based on the first normal vector surface, the space curve is performed. To predict, construct the first spatial curve.

As shown in FIG. 6 , P _a and P _b are the two endpoints of the line segment. In this embodiment, P _a and P _b are two vertices that are one side of a plane triangle, and the endpoint coordinates P _a of the straight line segment P _a P _b (x _a , y _a , z _a ), P _b (x _b , y _b , z _b ) and their normal vectors f _a (fx _a , fy _a , fz _a ), f _b (fx _b , fy _b , fz _b ), the method of solving the space curve formed by the straight line segment P _a P _b is as follows:

First, interpolate the normal vector along the straight line segment P _a P _b

As shown in Fig. 6, a series of discrete points P ₁ , P ₂ , ... P _k , ... are taken on the straight line segment P _a P _b , and the normal vector at each discrete point is calculated by using the linear interpolation method. Taking P _k (x _k , y _k , z _k ) as an example, f _xk in its normal vector f _k (f _xk , f _yk , f _zk ) can be expressed as:

The remaining coordinates f _yk and f _zk can be obtained by a similar method. It is worth noting that, in general, since the normal vectors f _a and f _b at both ends of the line segment are usually not coplanar, a series of normal vectors obtained in this step are also not coplanar. If the discrete points on the line segment P _a P _b are sufficiently dense, the normal vectors on the discrete points will form a normal vector surface that transitions from f _a to f _b . Next, the spatial curve from P _a to P _b will be reconstructed on this surface.

Subsequently, the spatial curve predicts:

As shown in Figure 7, since the points P _a and P _b are the two vertices of the original plane triangle, the final reconstructed space surface must pass through the points P _a and P _b , so there is a passing point P _a and f _a is the normal vector , which can be used as _a linear approximation of the reconstructed surface in the neighborhood of Pa. The ray (P ₁ , f ₁ ) with P ₁ as the starting point and f ₁ as the direction vector intersects the plane at point Q ₁ . Q ₁ is actually an estimate of the intersection of the ray (P ₁ , f ₁ ) and the reconstructed surface, And there is a certain error with the real intersection. Using the same method, take f ₁ as the normal vector as the tangent plane at point Q ₁ , and then find the intersection point Q ₂ with the ray (P ₂ , f ₂ ), and then find out Q ₃ , . . . , until Q _b .

In theory, P _b should coincide with Q _b , so this error needs to be corrected. Therefore, in an embodiment, the step of performing spatial curve prediction based on the first normal vector surface, and constructing the first spatial curve further includes: performing error correction on the constructed first spatial curve.

Finally, error correction:

As shown in FIG. 8 , the distance error between the estimated value Q _b and the true value P _b is e _b =|Q _b −P _b |. Since the errors are cumulative, corrections to the previous estimates are required. Taking Q _k as an example, its distance error e _k can be approximately expressed as:

Then the corrected coordinates of Q _k are:

Using this method to correct all the estimated points, a space curve generated by a line segment P _a P _b can be obtained. Therefore, the final reconstructed surface passes through the point Q _k ', and the normal vector of this point can be approximated by f _k .

In one embodiment, the step of constructing a plurality of second space curves and third space curves based on the coordinates and normal vector lines of each point of each of the first space curves corresponding to the plane triangle includes: from the Each of the first space curves corresponding to the two sides of the plane triangle extracts a point as a line segment endpoint, and connects the two line segment endpoints to obtain a connecting line segment; The second space curve corresponding to the connecting line segment; extracting a point from each of the two adjacent second space curves as a line segment endpoint, and connecting the two line segment endpoints to obtain a construction line segment; based on the construction line segment and the construction line segment The coordinates and normal vector of the end point of the line segment, and the third space curve corresponding to the construction line segment is constructed.

In this embodiment, the second space curve constructed based on these connecting line segments is approximately parallel visually.

In this embodiment, a point is first extracted from the first space curve corresponding to the two sides of the plane triangle as a line segment endpoint, and the two line segment endpoints are connected to obtain a connecting line segment, and a corresponding second space is constructed based on the connecting line segment. curve.

Specifically, curve reconstruction is performed on the two sides of the plane triangle, and then a point is taken on each of the two reconstructed curves to form a line segment. Since the endpoint coordinates of the line segment and the surface normal vector have been obtained, the method of the above embodiment can be used method, a space curve is generated based on the coordinates of the endpoints of the line segment and the normal vector, as shown in Figure 4(b). Then, continue to take points and connect lines on the generated space curve to generate the space curve, finally generate a curve network that meets the requirements, and complete the surface reconstruction, as shown in Figure 4(c).

In addition, adopt the same method as constructing the second space curve, as shown in FIG. 4C, extract a point from each of the two adjacent second space curves as the line segment endpoint, and connect the two line segment endpoints to obtain the constructed line segment; The construction line segment and the coordinates and normal vectors of the line segment endpoints of the construction line segment are used to construct a third space curve corresponding to the construction line segment.

In one embodiment, the step of calculating the reflected ray at the intersection of the ray on the plane sub-triangle using the law of reflection includes: calculating a surface normal vector at the intersection of the ray and the plane sub-triangle; Based on the surface normal vector at the intersection position and the ray, the reflection law is used to calculate the reflected ray at the intersection position of the ray on the plane sub-triangle.

In this embodiment, the intersection of the ray and the small triangular surfel set is calculated, and the surface normal vector at the intersection is solved.

If the ray does not intersect any small triangle in the set, the ray does not intersect the reconstructed surface; otherwise, find the small triangle that intersects the ray, calculate the coordinates of the intersection of the ray and the small triangle, and use the intersection as the ray and the reconstructed surface , as shown in Figure 5(a).

As shown in Figure 9, it is assumed that the ray intersects the plane sub-triangle ABC, and the intersection point is P. The vertex coordinates and normal vectors of the plane sub-triangle ABC are extracted, as shown in FIG. 9 , f _a , f _b , and f _c are the surface normal vectors at vertices A, B, and C, respectively. A line parallel to AB is drawn through the point P and intersected with BC, and the proportional coefficient of the intersection to BC is β (0≤β≤1); at the same time, a straight line parallel to BC is made to intersect AB through the point P, and the proportion of the intersection to AB is γ (0≤γ≤1), the surface normal vector at point P can be approximately expressed as:

f _p =(1-β-γ)f _b +βf _c +γf _a

Finally, the surface normal vector and the incident ray at the intersection point are known, and the reflection line can be solved according to the reflection law as the reflection line of the ray and the reconstructed surface.

It should be understood that although the various steps in the flowchart of FIG. 1 are shown in sequence according to the arrows, these steps are not necessarily executed in the sequence shown by the arrows. Unless explicitly stated herein, the execution of these steps is not strictly limited to the order, and these steps may be performed in other orders. Moreover, at least a part of the steps in FIG. 1 may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily executed and completed at the same time, but may be executed at different times. The execution of these sub-steps or stages The sequence is also not necessarily sequential, but may be performed alternately or alternately with other steps or sub-steps of other steps or at least a portion of a phase.

Embodiment 2

In this embodiment, a surface reconstruction method based on a plane triangle and its vertex normal vector is provided, which can ensure the strict continuity and basic smoothness between the reconstructed surfaces of adjacent plane triangles while realizing the reconstruction of the curved surface. As shown in Figure 10, the method first calculates (or extracts) the point normal vectors of the three vertices of the triangle, and uses this information to reconstruct the curve of an edge of the triangle, as shown in Figure 4(a); Take a point on each of the two curves, connect them into a line segment, and reconstruct the line segment, as shown in Figure 4(b). curve until a curve network that meets the user's needs is formed, as shown in Figure 4(c).

The solution process of the intersection of the ray and the surface and the reflection line: On the basis of the curve network obtained by the above method, firstly obtain the set of small plane triangles, and calculate the intersection of the ray and the set. If it intersects, find the small triangle where the intersection is located and the position of the intersection, as shown in Figure 5(a); then, use the normal vector of the vertex of the small triangle to reconstruct the normal vector of the intersection position, as shown in Figure 5(b); finally, Use the law of reflection to calculate the reflected rays at the intersection of the rays, as shown in Figure 5c).

The following describes the calculation process of vertex normal vector interpolation, curve and surface reconstruction, and intersection of rays and surfaces with reference to the accompanying drawings.

(1) Get/calculate the normal vector of the triangle vertex

If the true value of the normal vector of the vertex of the triangle can be obtained, the data can be used directly; otherwise, the normal vector of the vertex needs to be calculated using the relevant information of the common vertex plane triangle as an estimate of its true value, as shown in Figure 11. There are many such methods in the existing literature, which can be flexibly selected.

(2) Reconstructing space curve based on line segment vertex and normal vector information

Known the coordinates of the end points of the straight line segment P _a P _b P _a (x _a , y _a , z _a ), P _b (x _b , y _b , z _b ) and their normal vectors f _a (f _xa , f _ya , f _za ), f _b (f _xb , f _yb , f _zb ), the method for solving the space curve formed by the straight line segment P _a P _b is as follows.

① Interpolate the normal vector along the straight line segment P _a P _b

As shown in Fig. 6, a series of discrete points P ₁ , P ₂ , ... P _k , ... are taken on the straight line segment P _a P _b , and the normal vector at each discrete point is calculated by using the linear interpolation method. Taking P _k (x _k , y _k , z _k ) as an example, f _xk in its normal vector f _k (f _xk , f _yk , f _zk ) can be expressed as:

The remaining coordinates f _yk and f _zk can be obtained by a similar method. It is worth noting that in general, since the normal vectors f _a and f _b at both ends of the line segment are usually not coplanar, the series of normal vectors obtained in step ① are also not coplanar. If the discrete points on the line segment P _a P _b are sufficiently dense, the normal vectors on the discrete points will form a normal vector surface that transitions from f _a to f _b . Next, the spatial curve from P _a to P _b will be reconstructed on this surface.

②Space curve prediction

As shown in Figure 7, since the points P _a and P _b are the two vertices of the original plane triangle, the final reconstructed space surface must pass through the points P _a and P _b , so there is a passing point P _a and f _a is the normal vector , which can be used as _a linear approximation of the reconstructed surface in the neighborhood of Pa. The ray (P ₁ , f ₁ ) with P ₁ as the starting point and f ₁ as the direction vector intersects the plane at point Q ₁ . Q ₁ is actually an estimate of the intersection of the ray (P ₁ , f ₁ ) and the reconstructed surface, And there is a certain error with the real intersection. Using the same method, take f ₁ as the normal vector as the tangent plane at point Q ₁ , and then find the intersection point Q ₂ with the ray (P ₂ , f ₂ ), and then find out Q ₃ , . . . , until Q _b . In theory, P _b should coincide with Q _b , so this error needs to be corrected.

③Error correction

As shown in FIG. 8 , the distance error between the estimated value Q _b and the true value P _b is e _b =|Q _b −P _b |. Since the errors are cumulative, corrections to the previous estimates are required. Taking Q _k as an example, its distance error e _k can be approximately expressed as:

Then the corrected coordinates of Q _k are:

Q _k '=Q _k -e _k f _k

Using this method to correct all the estimated points, a space curve generated by a line segment P _a P _b can be obtained. It can be considered that the final reconstructed surface passes through the point Q _k ', and the normal vector of this point can be approximated by f _k .

(3) Connect line segments on adjacent spatial curves and reconstruct the curve

Using the method of step (2), curve reconstruction is performed on the two sides of the original plane triangle. Then, take a point on each of the two reconstructed curves and connect them into line segments. Since the endpoint coordinates of the line segment and the surface normal vector have been obtained, the method of step (2) can be used to generate a space curve, as shown in Figure 4(b).

(4) According to the actual needs of the user, continue to take points and connect lines on the generated space curve to generate the space curve, and finally generate a curve network that meets the requirements, and complete the surface reconstruction, as shown in Figure 4(c).

How to solve the intersection of ray and surface and reflection line

(1) On the basis of the curve network shown in Fig. 4(c), a small triangular surface element set is constructed, as shown in Fig. 5(a).

(2) Calculate the intersection of the ray and the small triangular surface element set, and solve the surface normal vector at the intersection point

If the ray does not intersect any small triangle in the set, the ray does not intersect the reconstructed surface; otherwise, find the small triangle that intersects the ray, calculate the coordinates of the intersection of the ray and the small triangle, and use the intersection as the ray and the reconstructed surface , as shown in Figure 5(a).

Suppose that the ray intersects the small triangle ABC at P. The vertex coordinates and normal vector of the small triangle are extracted, as shown in FIG. 9 , f _a , f _b , and f _c are the surface normal vectors at vertices A, B, and C, respectively. A line parallel to AB is drawn through the point P and intersected with BC, and the proportional coefficient of the intersection to BC is β (0≤β≤1); at the same time, a straight line parallel to BC is made to intersect AB through the point P, and the proportion of the intersection to AB is γ (0≤γ≤1), the surface normal vector at point P can be approximately expressed as:

f _p =(1-β-γ)f _b +βf _c +γf _a

(3) The surface normal vector and the incident ray at the intersection point are known, and the reflection line can be solved according to the law of reflection as the reflection line between the ray and the reconstructed surface.

Embodiment 3

In this embodiment, as shown in FIG. 2, a curved surface reflection line calculation device is provided, including:

a plane triangle determination module 210, configured to determine a plane triangle;

a first space curve construction module 220, configured to construct a first space curve corresponding to each side of the plane triangle;

a first coordinate and normal vector acquisition module 230, configured to acquire the coordinates and normal vectors of each point forming the first space curve;

The second space curve building module 240 is configured to build a plurality of second space curves and third space curves based on the coordinates and normal vector lines of each point of each of the first space curves corresponding to the plane triangle, wherein each of the The endpoints of both ends of the second space curve are located on two adjacent first space curves, and the endpoints of both ends of each of the third space curves are located on two adjacent second space curves;

a sub-triangle dividing module 250, configured to divide the area where the plane triangle is located into a plurality of plane sub-triangles based on each of the second space curves and each of the third space curves;

a ray acquisition module 260, configured to acquire rays;

an intersecting sub-triangle determining module 270, configured to determine a plane sub-triangle intersecting with the ray;

The reflected ray calculation module 280 is configured to use the reflection law to calculate the reflected ray at the intersection of the ray on the plane sub-triangle.

In one embodiment, the first space curve building module includes:

a vertex normal vector calculation unit for calculating the normal vectors of the three vertices of the plane triangle;

A first space curve construction unit, configured to construct a first space curve corresponding to the sides of the plane triangle according to the coordinates and normal vectors of the vertices of the sides of the plane triangle.

For the specific limitation of the device for calculating the reflection line on the curved surface, please refer to the limitation on the method for calculating the reflection line on the curved surface above, which will not be repeated here. Each unit in the above-mentioned curved surface reflection line computing device may be implemented in whole or in part by software, hardware, and combinations thereof. The above units may be embedded in or independent of the processor in the computer device in the form of hardware, or may be stored in the memory of the computer device in the form of software, so that the processor can call and execute the operations corresponding to the above units.

Embodiment 4

In this embodiment, a computer device is provided. Its internal structure diagram can be shown in Figure 3. The computer equipment includes a processor, memory, a network interface, a display screen, and an input device connected by a system bus. Among them, the processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium, an internal memory. The non-volatile storage medium stores an operating system and a computer program, and the non-volatile storage medium deploys a database. The internal memory provides an environment for the execution of the operating system and computer programs in the non-volatile storage medium. The network interface of the computer device is used to communicate with other computer devices on which application software is deployed. The computer program, when executed by the processor, implements a curved surface reflection line calculation method. The display screen of the computer equipment may be a liquid crystal display screen or an electronic ink display screen, and the input device of the computer equipment may be a touch layer covered on the display screen, or a button, a trackball or a touchpad set on the shell of the computer equipment , or an external keyboard, trackpad, or mouse.

Those skilled in the art can understand that the structure shown in FIG. 3 is only a block diagram of a part of the structure related to the solution of the present application, and does not constitute a limitation on the computer equipment to which the solution of the present application is applied. Include more or fewer components than shown in the figures, or combine certain components, or have a different arrangement of components.

In one embodiment, a computer device is provided, including a memory and a processor, wherein the memory stores a computer program, and it is characterized in that, when the processor executes the computer program, the above-mentioned method for calculating curved surface reflection lines is implemented the steps in any one of the examples.

Embodiment 5

In this embodiment, a computer-readable storage medium is provided, and a computer program is stored thereon, and when the computer program is executed by a processor, the steps of any one of the foregoing methods for calculating curved surface reflection lines are implemented.

Those of ordinary skill in the art can understand that all or part of the processes in the methods of the above embodiments can be implemented by instructing relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage In the medium, when the computer program is executed, it may include the processes of the above-mentioned method embodiments. Wherein, any reference to memory, storage, database or other medium used in the various embodiments provided in this application may include non-volatile and/or volatile memory. Nonvolatile memory may include read only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous chain Road (Synchlink) DRAM (SLDRAM), memory bus (Rambus) direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

The technical features of the above embodiments can be combined arbitrarily. In order to make the description simple, all possible combinations of the technical features in the above embodiments are not described. However, as long as there is no contradiction in the combination of these technical features It is considered to be the range described in this specification.

The above-mentioned embodiments only represent several embodiments of the present application, and the descriptions thereof are specific and detailed, but should not be construed as a limitation on the scope of the invention patent. It should be pointed out that for those skilled in the art, without departing from the concept of the present application, several modifications and improvements can be made, which all belong to the protection scope of the present application. Therefore, the scope of protection of the patent of the present application shall be subject to the appended claims.

Claims (10)

1. a curved surface reflection line calculation method, is characterized in that, comprises: Determine the plane triangle; constructing a first space curve corresponding to each side of the plane triangle; obtaining the coordinates and normal vectors of each point forming the first space curve; A plurality of second space curves and third space curves are constructed based on the coordinates and normal vector lines of each point of each of the first space curves corresponding to the plane triangle, wherein the endpoints of both ends of each of the second space curves are located at On the two adjacent first space curves, the endpoints of both ends of each of the third space curves are located on the two adjacent second space curves; dividing the area where the plane triangle is located into a plurality of plane sub-triangles based on each of the second space curves and each of the third space curves; get rays; determining the planar sub-triangle intersecting the ray; The reflected ray at the intersection of the ray on the plane sub-triangle is calculated using the law of reflection. 2. The method according to claim 1, wherein the step of constructing the first space curve corresponding to each side of the plane triangle comprises: Calculate the normal vectors of the three vertices of the planar triangle; The first space curve corresponding to the sides of the plane triangle is constructed according to the coordinates and normal vectors of the vertices of the sides of the plane triangle. 3. The method according to claim 2, wherein the step of constructing the first space curve corresponding to the sides of the plane triangle according to the coordinates and normal vectors of the vertices of the sides of the plane triangle include: Taking the coordinates of the vertices of the sides of the plane triangle as the two endpoints of the first line segment, performing normal vector interpolation along one end of the first line segment to the other end to obtain a first normal vector surface; Based on the first normal vector surface, a space curve prediction is performed to construct the first space curve. 4. The method according to claim 3, wherein the step of performing spatial curve prediction based on the first normal vector surface, and constructing the first spatial curve further comprises: Error correction is performed on the constructed first space curve. 5 . The method according to claim 1 , wherein the construction of a plurality of second space curves and third The steps for a space curve include: Extract a point from the first space curve corresponding to the two sides of the plane triangle as a line segment endpoint, and connect the two line segment endpoints to obtain a connecting line segment; constructing a second space curve corresponding to the connecting line segment based on the connecting line segment and the coordinates and normal vectors of the line segment endpoints of the connecting line segment; A point is extracted from each of the two adjacent second space curves as a line segment endpoint, and the two line segment endpoints are connected to obtain a construction line segment; Based on the construction line segment and the coordinates and normal vectors of the line segment endpoints of the construction line segment, a third space curve corresponding to the construction line segment is constructed. 6. The method according to any one of claims 1-5, wherein the step of calculating the reflected ray at the intersection of the ray on the plane sub-triangle using the law of reflection comprises: Calculate the surface normal vector of the intersection of the ray and the plane sub-triangle; Based on the surface normal vector at the intersection position and the ray, the reflection law is used to calculate the reflected ray at the intersection position of the ray on the plane sub-triangle. 7. A curved surface reflection line computing device, characterized in that, comprising: The plane triangle determination module is used to determine the plane triangle; a first space curve building module, configured to build a first space curve corresponding to each side of the plane triangle; a first coordinate and normal vector acquisition module, used to acquire the coordinates and normal vectors of each point forming the first space curve; The second space curve building module is configured to build a plurality of second space curves and third space curves based on the coordinates and normal vector lines of each point of each of the first space curves corresponding to the plane triangle, wherein each of the The end points of both ends of the second space curve are located on two adjacent first space curves, and the end points of both ends of each of the third space curves are located on two adjacent second space curves; a sub-triangle dividing module, configured to divide the area where the plane triangle is located into a plurality of plane sub-triangles based on each of the second space curves and each of the third space curves; A ray acquisition module for acquiring rays; an intersecting sub-triangle determination module, configured to determine a plane sub-triangle intersecting with the ray; The reflected ray calculation module is configured to use the reflection law to calculate the reflected ray at the intersection of the ray on the plane sub-triangle. 8. The apparatus according to claim 7, wherein the first space curve building module comprises: a vertex normal vector calculation unit for calculating the normal vectors of the three vertices of the plane triangle; A first space curve construction unit, configured to construct a first space curve corresponding to the sides of the plane triangle according to the coordinates and normal vectors of the vertices of the sides of the plane triangle. 9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein the processor implements the steps of the method according to any one of claims 1 to 6 when the processor executes the computer program . 10. A computer-readable storage medium on which a computer program is stored, characterized in that, when the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

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